Spatially resolved measurement of helium atom emission line spectrum in scrape-off layer of Heliotron J by near-infrared Stokes spectropolarimetry

For plasma spectroscopy, Stokes spectropolarimetry is used as a method to spatially invert the viewing-chord-integrated spectrum on the basis of the correspondence between the given magnetic field profile along the viewing chord and the Zeeman effect appearing on the spectrum. Its application to fusion-related toroidal plasmas is, however, limited owing to the low spatial resolution as a result of the difficulty in distinguishing between the Zeeman and Doppler effects. To resolve this issue, we increased the relative magnitude of the Zeeman effect by observing a near-infrared emission line on the basis of the greater wavelength dependence of the Zeeman effect than of the Doppler effect. By utilizing the increased Zeeman effect, we are able to invert the measured spectrum with a high spatial resolution by Monte Carlo particle transport simulation and by reproducing the measured spectra with the semiempirical adjustment of the recycling condition at the first walls. The inversion result revealed that when the momentum exchange collisions of atoms are negligible, the velocity distribution of core-fueling atoms is mainly determined by the initial distribution at the time of recycling. The inversion result was compared with that obtained using a two-point emission model used in previous studies. The latter approximately reflects the parameters of atoms near the emissivity peak.

apparent relative intensities of the 19 transitions 1,2 , and the apparent intensities of the π components are smaller than those of the σ components in Fig. S1. Figure S1. π and σ components of the HeI 2 3 S-2 3 P emission line spectrum measured in the direction perpendicular to the magnetic field in a glow discharge plasma at 300 Pa under uniform magnetic fields. The atomic temperature is evaluated to be approximately 0.1 eV. Zero levels are shifted for the spectra at 1-3 T.

NIR Stokes spectropolarimetry system
We used an NIR Stokes spectropolarimetry system illustrated in Fig. S2a designed for use with a single viewing chord. Emission from the plasma is decomposed to the orthogonal linear polarization components I0 and I90 using a polarization beam splitter (3×10 -3 extinction ratio). I0 and I90 are transferred via different optical fibers and injected into a Czerny-Turner type spectrometer (Horiba Jovin-Yvon THR1000; 1 m focal length, 2 nd -order diffraction with 720 grooves/mm grating, f/7.5).
The spectrometer is equipped with an entrance double slit (100 µm width and 2.54 mm pitch), and two sets of seven bundled optical fibers (230/250 µm core/cladding diameters, 0.22 NA) separately carrying I0 and I90 are aligned along the double slits. At the exit port of the spectrometer, the spectral images of I0 and I90 that slightly shifted in the wavelength direction are superposed. The images are resized by 1/7 and 2.2 times in the slit and wavelength directions, respectively, using two planoconvex cylindrical lenses. The resized images are recorded with an InGaAs linear detector (Hamamatsu G9206-512W; 0.9-2.1 µm sensitivity range, 512 pixels, 25 µm×250 µm pixel size, -20 o C, 15 bit).
For the InGaAs linear detector, we evaluated the standard deviation of the dark noise for all the pixels and excluded flawed pixels having standard deviations that are significantly larger than statistically expected values. Figure S2b shows a histogram of the standard deviation evaluated using nine consecutive frames measured with the exposure time of 120 ms without light injection. Given that the dark noise follows a normal distribution, its standard deviation follows a Gamma distribution 3 . We fitted the histogram using a Gamma distribution with N = 9, where N is the number of samples. The fitting curve is shown in the figure. 72 pixels having a large standard deviation in the range of the significant level of 0.02 of the fitting curve were excluded from analysis.
The intensities of the measured I0 and I90 were absolutely calibrated using diffuse reflected light from a stabilized Globar lamp (Thorlabs SLS203LM). We pre-calibrated the spectral irradiance of the lamp and regarded the diffuse reflected light unpolarized. The calibration accuracy was confirmed using the ratio I90/I0 of the HeI 2 3 S-2 3 P spectrum measured at 3 T shown in Fig. S1. In the wavelength range 1083.00-1083.05 nm, the spectrum has only the π component and I90/I0 can be regarded as the extinction ratio. As shown in Fig. S2c, the average ratio is 9(2)×10 -3 , where the number in the bracket denotes the standard error. The evaluated extinction ratio is smaller than the dark noise in Fig. 3a, which is ~2×10 -2 in the scale of the figure, and we neglected mixing of I0 and I90 in the analysis.
The wavelengths of the measured I0 and I90 were absolutely calibrated using a HeI 2 3 S-2 3 P emission line spectrum from a helium glow discharge lamp without the magnetic field (Electro-Technic Products). The given wavelengths at the two fine structure peaks were used neglecting their Doppler shifts. A NeI emission line spectrum of a neon glow discharge lamp (Electro-Technic Products) was regarded as the instrumental functions and the instrumental width was approximately 45 pm for both I0 and I90.

Definition of polar and azimuthal angles
We define the polar angle γ and azimuthal angle χ of the magnetic field B with respect to the observer as illustrated in Fig. S3.  Table S1. The heating power P was determined from the experimental condition.
The edge electron density at r/a = 0.8, where r is the minor radius and a is that at the LCFS, and thermal diffusion coefficient χ were determined so as to minimize the differences in Te and ne  Fig. S4b can be overestimated. The overestimated Te and ne will reduce the penetration depth of atoms and to compensate for the effect, T can be overestimated. Thermal diffusion coefficient χ (m 2 s -1 )

2.5
Particle diffusion coefficient D (m 2 s -1 ) 0.5 Figure S4. The calculation was conducted in the #10.5 poloidal plane using a 2d3v space. The calculation region in real space is the same as that of EMC3-EIRNENE, which is in the ranges of  ) os where v is the velocity, θ is the polar angle of the velocity with respect to the surface normal, is the solid angle of the velocity made by θ (= 0-π/2) and the azimuthal angle φ where m is the mass of atoms and kB is the Boltzmann constant. The φ-component of the velocity was assumed to be uniformly distributed.
where q is an index of an excited state, Cpq and Fpq are the electron-impact excitation and deexcitation rate coefficients, respectively, Sp is the electron-impact ionization rate coefficient, and Apq is the spontaneous emission coefficient. Cpq, Fpq, and Sp are the functions of Te and ne at the position of the previous step xi. The data of Cpq, Fpq, Sp, and Apq are taken from the CR-model code 6 . The mean free path of the atoms ∆xi is evaluated using the expression where ξ is the uniform random variable ( 0 1 ξ ≤ ≤ ) and Σp(xi) is the total reaction rate at xi. The position of the atom is then translated in the direction of its velocity by a distance ∆xi. After the calculation of all the atoms, 3 2 P n , f(vvc), and HeI 2 3 S-2 3 P emissivity and spectrum shape were evaluated using the total number of 2 3 P excited atoms and their velocities recorded at each grid.
where me and m are the masses of the electron and helium atom, respectively, E is the electron kinetic energy before the collision, and σel is the elastic-scattering cross section 11 . ∆E is approximately 9 meV at E = 50 eV, and the total energy transferred to the atoms in the SOL will be a fraction of the determined atomic temperature at the FWs T = 0.15 eV. Figure S6. Same as Fig. 4a with plotting mean free path of electron momentum exchange collision m λ .